II.2 Density Dependence and SingleSpecies Population Dynamics Anthony R. Ives OUTLINE 1. Three questions about the dynamics of single species 2. Density dependence 3. Endogenous population variability 4. Exogenous population variability 5. Returning to the three questions In ecology, population dynamics refers to how populations of a species change through time. The study of singlespecies population dynamics encompasses three general questions: (1) What explains the average abundance of a population? (2) What explains the ﬂuctuations in abundance of a population through time? and (3) How do average abundances and ﬂuctuations in abundance vary among populations in different geographic locations? Any of these questions can be asked of any population of any species, yet some populations pose particularly interesting challenges for one or more of the questions. Thus, ecologists often focus on populations that are remarkably large (pests) or small (endangered species), that have dramatic ﬂuctuations through time, or that vary markedly from one location to another. GLOSSARY density dependence. Densitydependent population growth occurs when the per capita population growth rate changes as the population density changes. Because it changes with population density , densitydependent growth is not exponential. dynamics. The dynamics of a population consists of the changes through time in the population size or a related measure such as density. endogenous variability. Endogenous population variability is driven by densitydependent factors that involve interactions among individuals in the system speciﬁed by a researcher. The system could consist of a single population or populations of interacting species. exogenous variability. Exogenous population variability is driven by factors outside the system that are not themselves inﬂuenced by population ﬂuctuations within the system. Examples include not only environmental factors such as weather but also the abundances of other species if the dynamics of these species is not affected by the focal species within the system. exponential population growth and decline. When the per capita population growth rate remains constant, the population experiences exponential growth or decline. Exponential population growth can also occur when the per capita population growth rate varies through time provided its average remains constant. intrinsic rate of increase. The intrinsic rate of increase is the maximum per capita population growth rate for a population with a stable age structure (i.e., the proportions of the population in different age groups remain the same). The intrinsic rate of increase is often achieved when the population is at low density. per capita population growth rate. The per capita population growth rate is the rate at which a population changes per individual in the population. It is often expressed as the natural logarithm of the ratio of population densities at consecutive sample times, log ex(t þ 1)=x(t). population. A population is a group of individuals of the same species occupying a speciﬁed geographic area over a speciﬁed period of time. The area may be ecologically relevant (an island) or irrelevant (political districts), and the boundaries may be porous , with individuals immigrating to and emigrating from the population. stability. Stability is deﬁned in many ways in ecology. In models of population dynamics, stability is generally used in two ways. First, when there is no environmental stochasticity, stability describes how populations change when they are around points or cycles. A stable point, for example, is one in which, if the population density is initially near the point, it will move generally closer to the point through time. Second, when there is environmental stochasticity, a more stable system is one in which population variability is small for a given level of environmental variability in the per capita population growth rate. There are additional ways that stability can be de ﬁned in model and real systems, which necessitate care in using the word stability. stochasticity. Stochasticity is random (unpredictable) variability that is described by a probability distribution giving the mean, variance, and other properties of the random process. 1. THREE QUESTIONS ABOUT THE DYNAMICS OF SINGLE SPECIES The three broad questions about singlespecies population dynamics boil down to: What explains the abundance of a population and changes in abundance through time and space? As an example of the ﬁrst question, we could ask why, unfortunately, there are more mosquitoes than moose in Wisconsin. The answer might seem simple; moose are so much bigger than mosquitoes, they simply occupy more space and need more food. The question becomes more difﬁcult, however , when asking why the roughly 60 species of mosquitoes in Wisconsin differ hugely in...

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